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Russian Journal of Nonlinear Dynamics, 2022, Volume 18, Number 4, Pages 681–707
DOI: https://doi.org/10.20537/nd221204
(Mi nd819)
 

Nonlinear engineering and robotics

A Nonholonomic Model and Complete Controllability of a Three-Link Wheeled Snake Robot

E. M. Artemovaa, A. A. Kilinba

a Ural Mathematical Center, Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
b Institute of Mathematics and Mechanics of the Ural Branch of RAS, ul. S. Kovalevskoi 16, Ekaterinburg, 620990 Russia
References:
Abstract: This paper is concerned with the controlled motion of a three-link wheeled snake robot propelled by changing the angles between the central and lateral links. The limits on the applicability of the nonholonomic model for the problem of interest are revealed. It is shown that the system under consideration is completely controllable according to the Rashevsky – Chow theorem. Possible types of motion of the system under periodic snake-like controls are presented using Fourier expansions. The relation of the form of the trajectory in the space of controls to the type of motion involved is found. It is shown that, if the trajectory in the space of controls is centrally symmetric, the robot moves with nonzero constant average velocity in some direction.
Keywords: nonholonomic mechanics, wheeled vehicle, snake robot, controllability, periodic control.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2022-889
Russian Science Foundation 21-71-10039
The work of A. A. Kilin (Sections 1–3) was performed at the Ural Mathematical Center (Agreement No. 075-02-2022-889). The work of E. M. Artemova (Section 4, Appendices) was supported by the Russian Science Foundation (No. 21-71-10039) and was supported in part by the Moebius Contest Foundation for Young Scientists.
Received: 15.09.2022
Accepted: 16.11.2022
Bibliographic databases:
Document Type: Article
MSC: 37J60, 70Exx, 70Kxx
Language: english
Citation: E. M. Artemova, A. A. Kilin, “A Nonholonomic Model and Complete Controllability of a Three-Link Wheeled Snake Robot”, Rus. J. Nonlin. Dyn., 18:4 (2022), 681–707
Citation in format AMSBIB
\Bibitem{ArtKil22}
\by E. M. Artemova, A. A. Kilin
\paper A Nonholonomic Model and Complete Controllability
of a Three-Link Wheeled Snake Robot
\jour Rus. J. Nonlin. Dyn.
\yr 2022
\vol 18
\issue 4
\pages 681--707
\mathnet{http://mi.mathnet.ru/nd819}
\crossref{https://doi.org/10.20537/nd221204}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4527645}
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  • https://www.mathnet.ru/eng/nd/v18/i4/p681
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